Seminars Sorted by Series

Proteins with knots in their native state were discovered few years ago. Analysis of the entire protein data base indicates that there are quite a few proteins with knots, particularly with slip knots, but still the fraction of proteins with knots...

We discuss some geometric and topological methods that are applied to overcome the large gap problem in Arnold diffusion for a priori unstable Hamiltonian systems. The geometric methods rely on the theory of normally hyperbolic invariant manifolds...

For a planar domain, a finite point configuration is said to be caging, if the set of Euclidean motions of the domain not hitting the point configuration is bounded. Caging configurations are important in robotics and are a popular topic in...

Optical fields propagating in three-dimensional free space are complex scalar fields, and typically contain nodal lines (optical vortices) which may be thought of as interference fringes. Random wave fields, representing speckle patterns randomly...

This will be a report on topics related to topological complexity (TC), introduced by Michael Farber in 2003 as a numerical measure of the complexity of robot motion planning problems. TC of real projective space P^n (lines through the origin in...

The ordinary homology of a subset S of Euclidean space depends only on its topology. By systematically organizing homology of neighborhoods of S, we get quantities that measure the shape of S, rather than just its topology. These quantities can be...

The space of all positions of n disks of radius r in a bounded region has long been studied from the points of view of statistical mechanics and probability. A phase transition is known to occur from simulations, but this is still mysterious to...

Can we use computational algorithms to make accurate predictions of physical phenomena? In this talk, intended for non-experts, I will give examples where complicated space-time phenomena can be exquisitely captured with simple computational...

DNA copy number abnormalities (CNAs) play an important role in cancer, and are associated with tumor progression as well as clinical outcome. Using microarray based comparative genomic hybridization (CGH), analysis of CNAs across large cohorts of...

High-dimensional data sets often carry meaningful low-dimensional structures. There are different ways of extracting such structural information. The classic (circa 2000, with some anticipation in the 1990s) strategy of nonlinear dimensionality...

How do things hold up? What are the geometric ideas that are involved? One of the principles can be seen with simple models, where sticks are suspended in mid-air with inextendable cables. These were called tensegrities by Buckminster Fuller...

In this talk we discuss the recent area of topological data analysis (TDA) from a probabilistic perspective. The talk falls under two parts. The first part of the talk considers a classic object in topology and geometry, a (Whitney) stratified space...

Topological defects pervade a wide range of physical systems, from superconductors to smectic liquid crystals. The behavior and interactions of such singularities impart many materials with a wealth of rich behavior. Just as flux vortices in the...

This will be a survey talk on equivariant topology methods and how to use them in discrete geometry and combinatorics, based on examples.

Computation of cycles representing classes of homology groups is a fundamental problem arising in applications such as parameterization, feature identification, topology simplification, and data analysis. Variations of the classical Smith Normal...

Suppose a large number of voters have each rated or compared a small subset of a large number of alternatives, how could we rank the alternatives based on these data? The rank aggregation problem is fraught with famous difficulties --- Arrow's...

The number of energetically stable structures that a system of N particles can form grows exponentially with N. Stabilizing any one structure over all others is thus a challenging problem. We consider a system of N spherical colloidal particles that...

I derive a new set of bounds on the percolation threshold of a class of continuum percolation models consisting overlapping convex hyperparticles in d-dimensional Euclidean space. The bounds converge to one another as the space dimension increases...